In an ideal intrinsic semiconductor mobility is determined by lattice scattering; that is, collisions between lattice waves (phonons) and electron waves (electrons). In an actual intrinsic specimen there are always some impurity atoms which may dominate scattering at low temperatures when phenons are quiescent, but at higher temperatures lattice scattering, particularly by optical phonons, is dominant. At cryogenic temperatures (e.g., T=4 to 77 K) ionized impurity scattering does indeed dominate mobility and, in fact, for a given impurity concentration follows a T.sup.3/2 law for a uniformly doped sample. In addition, the theory of Brooks and Herring predicts, and an experiment confirms, that as a result of electron-electron scattering at a given temperature, mobility decreases with increasing impurity concentration, and for each doping level there is a theoretical maximum mobility. Finally, it is known that, in general, the mobility of electrons (and hence n-type semiconductors) is greater than the mobility of holes (and hence p-type semiconductors).
A highly doped n-type semiconductor, therefore, typically suffers from low mobility both at low temperatures (e.g., 4 K) due to ionized-impurity scattering from donors used to dope the specimen, and at high temperatures (e.g., 300 K) due to electron-electron scattering and electron-phonon scattering. Thus, the highest mobility semiconductors tend to be low doped so as to reduce both electron-electron scattering and ionized-impurity scattering. But low doping levels cause commensurately low conductivity at room temperature due to a dearth of carriers and at cryogenic temperatures due to carrier freeze-out.
Consider the compound semiconductor GaAs is an example. N-type samples typically exhibit room temperature mobilities of about 6,800 to 2,800 cm.sup.2 V.sup.-1 sec.sup.-1 for doping levels of 10.sup.15 to 10.sup.18 /cm.sup.3. But mobility is highly temperature dependent. A GaAs sample doped to 10.sup.17 /cm.sup.3 may have a mobility of several thousand at room temperature, but at liquid helium temperatures the mobility may be less than a hundred. Extremely high mobilities in GaAs (e.g., 10.sup.5 cm.sup.2 V.sup.-1 sec.sup.-1) have been attained by vapor phase epitaxy in isolated cases by utilizing extremely low doped samples (e.g., 10.sup.13 /cm.sup.3). As mentioned previously, however, GaAs with such low doping levels suffers from low conductivity.